You may need to use the appropriate appendix table to answer this question. According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.t Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800. (a) What is the probability that a household in Maryland has an annual income of $110,000 or more? (Round your answer to four decimal places.) 0.1562 V (b) What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.) 0.2236 (c) What is the probability that a household in Maryland has an annual income between $60,000 and $70,000? (Round your answer to four decimal places.) 0.1133 (d) What is the annual income (in $) of a household in the eighty-sixth percentile of annual household income in Maryland? (Round your answer to the nearest cent.) $
You may need to use the appropriate appendix table to answer this question. According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.t Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800. (a) What is the probability that a household in Maryland has an annual income of $110,000 or more? (Round your answer to four decimal places.) 0.1562 V (b) What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.) 0.2236 (c) What is the probability that a household in Maryland has an annual income between $60,000 and $70,000? (Round your answer to four decimal places.) 0.1133 (d) What is the annual income (in $) of a household in the eighty-sixth percentile of annual household income in Maryland? (Round your answer to the nearest cent.) $
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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
Transcribed Image Text:**Understanding Probability and Percentiles in Household Income Distributions**
In this exercise, we explore the distribution of annual household income in Maryland, based on data from *Money* magazine, which reported that Maryland had the highest median annual household income of any state in 2018 at $75,847. The income follows a normal distribution with the given median and a standard deviation of $33,800.
**Questions and Solutions:**
(a) **Probability of Income $110,000 or More**
We want to find the probability that a household in Maryland has an annual income of at least $110,000. Using the normal distribution, this probability is:
- **Probability:** 0.1562
(b) **Probability of Income $50,000 or Less**
Next, we calculate the probability that a household has an annual income of $50,000 or less.
- **Probability:** 0.2236
(c) **Probability of Income Between $60,000 and $70,000**
We need to find the probability that a household's income falls between $60,000 and $70,000.
- **Probability:** 0.1133
(d) **Eighty-Sixth Percentile of Annual Household Income**
Finally, determine the annual income corresponding to the eighty-sixth percentile. This means that 86% of households earn less than this amount.
- **Eighty-Sixth Percentile Income:** Not provided (requires calculation)
This analysis provides insights into the distribution and likelihood of various income levels in Maryland, aiding in economic planning and policy-making.
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